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Theorem con34b 284
Description: Contraposition. Theorem *4.1 of [WhiteheadRussell] p. 116. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
con34b  |-  ( (
ph  ->  ps )  <->  ( -.  ps  ->  -.  ph ) )

Proof of Theorem con34b
StepHypRef Expression
1 con3 128 . 2  |-  ( (
ph  ->  ps )  -> 
( -.  ps  ->  -. 
ph ) )
2 ax-3 7 . 2  |-  ( ( -.  ps  ->  -.  ph )  ->  ( ph  ->  ps ) )
31, 2impbii 181 1  |-  ( (
ph  ->  ps )  <->  ( -.  ps  ->  -.  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 177
This theorem is referenced by:  mtt  330  pm4.14  562  dfom2  4838  weniso  6066  dfsup2  7438  wemapso2lem  7508  pwfseqlem3  8524  indstr  10534  rpnnen2  12813  algcvgblem  13056  isirred2  15794  isdomn2  16347  ist0-3  17397  mdegleb  19975  dchrelbas4  21015  toslub  24179  tosglb  24180  raldifsni  26671  isdomn3  27438  conss34  27559  dff14a  28009
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178
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